6 papers
Finite-State Mutual Dimension
Adam Case, Jack H. Lutz
In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the finite-state dimension (a finite-state version of algorithmic dimension) of a sequence and,…
The intersection of algorithmically random closed sets and effective dimension
Adam Case, Christopher P. Porter
In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of…
Bounded Turing Reductions and Data Processing Inequalities for Sequences
Adam Case
A data processing inequality states that the quantity of shared information between two entities (e.g. signals, strings) cannot be significantly increased when one of the entities…
Mutual Dimension and Random Sequences
Adam Case, Jack H. Lutz
If and are infinite sequences over a finite alphabet, then the lower and upper mutual dimensions and are the upper and lower densities of the algori…
Reachability Problems for Continuous Chemical Reaction Networks
Adam Case, Jack H. Lutz, D. M. Stull
Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but…
Mutual Dimension
Adam Case, Jack H. Lutz
We define the lower and upper mutual dimensions and between any two points and in Euclidean space. Intuitively these are the lower and upper densiti…